Beyond the God Particle (25 page)

Our microscope has a lens system. This is made of Van Leeuwenhoek's perfectly spherical crystal lenses in a configuration of Lister's chromatic aberration-free compound lens system. The lens system of the microscope collects some small amount of these scattered photons. It then focuses the collected photons to form an image, and the image is then presented to the eyeball of the observer.

So, the recipe for a microscope is

(1) Beam

(2) Target

(3) Detector = Lens system + eyeball

(4) Brain = Computer

OK, that's great! So now, let's just get a bigger and better Van Leeuwenhoek microscope with Lister's compound lens system and a bright beam of photons (higher luminosity), and let's go look at quarks! Unfortunately, it doesn't work quite that way. There are fundamental limits to how small an object we can see with an optical microscope. So, why can't an ordinary bio-lab microscope see a quark?

Recall our discussion in
chapter 2
where we talked about the size of a probe vs. the size of the target: In an optical microscope the light particles, photons, are the probes. Therefore, what limits the resolution of a microscope is the physical “size of the photons” in our beam. In general, if the particles in our particle beam are “bigger” than the object we want to see, we will not be able to form a focused image. This is a kind of golden rule of physics: To measure something small, you need a probe of the object that is smaller than the object itself.

But, you say, photons are small, aren't they? They are elementary particles, and you said they have no discernible structure. They are pinpoints. So why won't they work as a probe? This is where we encounter the wavelike nature of all quantum particles. In short, the quantum theory paradoxically says that all things that are particles are also waves. They are both and they are neither. If this seems like an almost untenable logical paradox, all we can say is “Welcome to the quantum world, which no one really understands but our students are trained to use.” This is the so-called “particle-wave-duality,” and quantum theory is very subtle, yet very emphatic about the meaning of this. Even Einstein tried to rewrite this principle, but failed.

In the case of light, as we have discussed in
chapter 2
, photons are indeed point-like particles, with no size whatsoever, pinpoint, but they are also waves. And, it is the size of the
wave motion
of these pinpoint particles, or the “wavelength” of the quantum wave, that determines the “size of a photon” as far as microscopes are concerned (see
figure 2.1
).
¹²
As we've seen, ordinary visible light has wavelengths in a range of around 0.00005 cm (5 × 10
^-5
cm). Therefore, optical microscopes cannot resolve small structures below a scale of about 0.0001 centimeters (10
^-4
cm), no matter how well fabricated they are.

As the demands upon the science of microscopy moved to observe shorter and shorter distance scales, and the finest of lenses and optical systems were developed, this brick wall of the wavelength of light was encountered. Optical microscopes won't work to see the detailed structure inside the cells of living organisms, or to see viruses, large macromolecules, the DNA molecule itself, and so forth. To do so, we need a particle beam made of something smaller than visible photons.

MICROSCOPES THAT DON'T USE LIGHT!

The weird particle-wave duality of the quantum theory also provides a solution to the problem of building a better microscope.

First, the quantum theory tells us that
all particles
are simultaneously waves. This means we can use any particle we want, and it need not be a photon. For example it can be an
electron
, one of the easiest of all particles to find—electrons are found orbiting the nucleus of every atom in the universe. Second, the quantum theory tells us exactly how much energy we have to endow an electron with to dial up any particular quantum wavelength that we want. Third, electrons have electric charge, and it's therefore easy to give them an energy kick with the right kind of device. With a little kick in energy, we can create any tiny quantum wavelength we want for electrons. And, finally, electrons, and other charged particles can be focused with “electromagnetic lenses.” Electrons are definitely particles, with mass and electric charge, and they have spin like little gyroscopes. Electrons are an ideal probe particle for the beam of a microscope.

The particle-wave duality of the photon was well understood by
the 1920s, but it was thought that this property belonged exclusively to photons. It was therefore a real shocker when people first realized that electrons are also both particles
and
waves. This idea was due to a young graduate student, Louis de Broglie, who was studying the new embryonic quantum theory of Planck, Bohr, Einstein, Heisenberg, and others at the Sorbonne in Paris in 1924. It was also known, thanks to Niels Bohr, that electrons had a certain wavelike behavior when they were trapped in atoms. But it was thought that this had to do with the particular orbital motion of electrons when they were bound to atoms and that it was not necessarily an intrinsic property of the electron itself.

De Broglie proposed, in his PhD thesis, that the electron, like the photon, is a quantum particle-wave under all circumstances. It should therefore be possible to observe the wavelike motion of untrapped or freely moving electrons as they coast along through space. One should be able to do an experiment that reveals the characteristic features of waves with electrons. These general features of waves are known as
diffraction
and
interference
, common wavelike behaviors seen in light, or even in water waves. De Broglie wrote down the relevant equations in his brief, three-page-long doctoral dissertation at the Sorbonne—the equations are really quite simple once you get the basic ideas of quantum theory in your head.

The distinguished old-guard faculty of the Sorbonne was astonished by the brevity and simplicity of de Broglie's idea, but they were also unable to comprehend it. They were ready to dismiss the doctoral thesis altogether and send poor de Broglie home. Alas, and fortunately, someone sent a copy of his thesis to Albert Einstein with a request for a second opinion. Einstein replied that the young man in question deserved a Nobel Prize more than a doctorate degree.

Indeed, the wave motion of freely moving electrons was shortly thereafter confirmed in 1927 in an experiment in the US at Bell Labs by Joseph Davisson and Lester Germer. Electrons were seen to undergo diffractive interference, like light waves, as they bounced off the surface of a crystalline metal. This was a stunning development. No one had ever previously questioned that electrons were anything but hard little particles that would only scatter and bounce like billiard balls. Electrons, like photons, were proven to be waves—actually, quantum particle-waves—the enigmatic way of quantum theory. And de Broglie was, in fact, awarded the Nobel Prize in
Physics in 1929. The pieces of the quantum puzzle were soon put together into a new reality—
all particles are waves at the same time!
¹³

The question before us now is “What does this do for microscopy?” For charged particles such as electrons (charge = –1), protons (charge = +1), and even muons (charge = –1), etc., their quantum wavelengths can be made arbitrarily small if we can get these particles to arbitrarily high energies. Each of these particles conveniently has a special “handle” on it, the electric charge, that allows us to grab a hold and accelerate it.
Any electrically charged particle placed in an electric field will be accelerated and will acquire more energy of motion (kinetic energy).
The particle draws this energy out of the electric field.

In principle there is no limit to how high an energy we can give to an electron, or a proton, or even a muon, though for any acceleration scheme we eventually hit severe practical problems. Much of the modern development of accelerators involves overcoming various technical challenges (though, as we saw with the Super Collider, we couldn't overcome the political or financial challenges). In summary, using accelerated charged particles instead of light, we should be able to make “microscopes” of virtually unlimited resolving power and magnification.

PARTICLE ACCELERATORS

An accelerator is a device that takes some particles of matter, essentially at rest, and through the process of
acceleration
, endows them with a high kinetic energy (energy of motion). Recall that we always need a beam of accelerated particles as the first stage of a microscope system. The accelerator provides the beam.

A slingshot is a primitive form of particle accelerator. It consists of a wishbone-shaped frame, usually a branch cut from a tree, to which a large rubber or elastic band (the sling) is attached. The user places a stone in the band and pulls it back, thus stretching it and increasing the
potential energy
of the rubber sling, with the stone in the sling. He then aims at the target and lets go. As the elastic band snaps back into its original form, the stone is accelerated. The potential energy in the stretched elastic band (the energy vested in stretching the band) is converted into the
kinetic energy
(energy of motion) of the stone. Beware: Slingshots are
very dangerous
and
you kids are advised not to play with them. For that matter, a gun is an accelerator, and it is much more dangerous. A car, a high-speed train, an airplane, a rocket ship are all people accelerators.

The physics of a slingshot is no different than that of a powerful proton, electron, or muon accelerator. The stone is replaced by a charged particle, such as an electron, and the sling band is replaced by an
electric field
.

ELECTRIC FIELDS ACCELERATE CHARGED PARTICLES

“Fields” are a central part of physics. You can't see fields, but they are there. They are real. They have energy, and they may or may not exert influence upon you. If a field has an influence on a particle, then we say that a particle is
coupled to the field
. “Electric charge” is the “coupling” of an electron or proton or muon to an electric or magnetic field. The field can then influence the motion of the particle, perhaps accelerating or de-accelerating it (electric field), or deflecting and diverting its direction of motion (electric or magnetic field).

The idea of “fields” began with gravity. Isaac Newton realized that there is a force of gravity between any two massive objects in the universe. He hypothesized that this force was attractive and proportional to the product of the masses of the objects. The strength of the force fell off with the separation of the objects according to the “inverse square law.” He further hypothesized exactly how strong this force is for any pair of massive particles by a simple formula. The simple formula is called Newton's universal gravitational force law. The term “universal” means that you can plug into the formula the masses of any two objects, and their distance of separation, and out of the formula pops the gravitational force between the two masses. With some remarkable mathematical analysis (Newton also invented the “Calculus” to analyze motion in a gravitational force), he discovered that this one simple and elegant formula for gravitational force precisely explained the motion of the moon in its orbit about the earth, the motion of all the planets in their orbits about the sun, as well as the rate at which apples (or anything else) fall from trees on the earth. This was a “grand unification” of our understanding of the force of gravity, as well as the laws of motion of all objects in nature by gravity.
¹⁴

About a hundred years after Newton's discoveries, it was realized that there are also
electric
and
magnetic
forces. It was in 1785 that Charles-Augustin de Coulomb discovered that a particle can exert a force (much stronger than gravity) upon another particle placed some distance away. Coulomb discovered that this force occurred when the particles have an attribute that was called “electric charge.” Most matter is electrically neutral, i.e., it has no detectable charge, so we don't immediately see the effect of this new force. However, it is possible to generate net electric charge on objects, and then the powerful new force becomes apparent. The strength of the force between charged objects “fell inversely as the square of the distance between them,” just like Newton's universal law of gravitation a hundred years earlier.
¹⁵

The concept of electric charge evolved shortly thereafter, involving major insights of Benjamin Franklin and others.
¹⁶
We all know how it goes: a positive charge will attract a negative charge, while positive (negative) will repel another positive (negative)—likes repel while opposites attract—“in love as in electrodynamics.” Today we also know that all elementary particles carry electric charges that can be measured and found to take on certain mathematical values. The charges found in nature are simple integer multiples of a basic quantity, called the fundamental charge, and that we call “e.” A neutron, for example, carries zero times the fundamental charge and is electrically neutral. An electron carries minus one times the fundamental charge, i.e., an electron has charge –e, and a proton carries plus one times this charge, i.e., a proton has charge +e.

The universe has, as far as we can discern, an equal balance of positively and negatively charged particles. Most all charges have assembled themselves within ordinary matter into atoms, in which negative electron charges for the most part cancel positive proton charges. The electrical neutrality of matter is testament to the very strong nature of electric force compared to gravity—if we strip electrons off (or add them to) atoms we get
ions
, which are effectively atoms with an excessive, or un-canceled, positive or negative charge. Stray electrons can eventually find their way to an ion and combine to make a neutral atom, and the world more or less re-neutralizes itself.